%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO463^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:55 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 18
% Syntax : Number of formulae : 189 ( 67 unt; 0 typ; 8 def)
% Number of atoms : 1488 ( 255 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 1968 ( 352 ~; 384 |; 13 &;1098 @)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 127 ( 127 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 63 usr; 16 con; 0-4 aty)
% ( 101 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 359 ( 0 sgn 72 !; 0 ?; 359 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s4: $i > $i > $o ).
thf(func_def_33,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
vNOT: $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
vAND: $o > $o > $o ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f46,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f47,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f48,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f47]) ).
thf(f51,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f52,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f51]) ).
thf(f53,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f59,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f60,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f61,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f62,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f64,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f72,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f73,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f74,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f75,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f91,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f92,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(flattening,[],[f48]) ).
thf(f99,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f100,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f101,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f102,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f113,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f114,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f115,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f129,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f52]) ).
thf(f130,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f131,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f137,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f101,f99,f114,f99,f99]) ).
thf(f138,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f131,f114,f99]) ).
thf(f140,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f130,f137,f138,f138]) ).
thf(f147,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ q ) ) ) ) ) ),
inference(definition_unfolding,[],[f113,f102,f138,f100,f140,f100,f140,f100,f100]) ).
thf(f149,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f129,f115]) ).
thf(f150,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( q @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( q @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f151,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( q @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( q @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ~ ( rel_s4 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( ( rel_s4 @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( q @ X1 ) ) )
| ( ( rel_s4 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( ( rel_s4 @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f167,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( q @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f170,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) )
| ~ ( rel_s4 @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
( $false
= ( ~ ( rel_s4 @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( q @ X1 )
| ~ ( rel_s4 @ sK1 @ X1 ) ) )
| ( $true
= ( ( p @ X2 )
| ~ ( rel_s4 @ sK1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( p @ X2 )
| ~ ( rel_s4 @ sK1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) )
| ( $true
= ( q @ X1 ) ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK1 @ X2 ) ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) )
| ( $true
= ( q @ X1 ) ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK1 @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK1 @ X2 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f191,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( ( ( q @ sK2 )
| ~ ( rel_s4 @ sK1 @ sK2 ) )
= $false )
| ( $true
= ( ( q @ X1 )
| ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $true
= ( ( q @ X1 )
| ~ ( rel_s4 @ sK1 @ X1 ) ) )
| ( ( ~ ( rel_s4 @ sK1 @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( ( q @ sK2 )
= $false )
| ( $true
= ( ( q @ X1 )
| ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( ( q @ sK2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( ( q @ sK2 )
= $false )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( ( ~ ( rel_s4 @ sK1 @ sK2 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f198,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK1 @ sK2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $true
= ( rel_s4 @ sK1 @ sK2 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f201,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK3 ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f212,plain,
( ( ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK4 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f201]) ).
thf(f213,plain,
( ( $false
= ( ( p @ sK3 )
| ~ ( rel_s4 @ sK1 @ sK3 ) ) )
| ( $false
= ( ( q @ sK4 )
| ~ ( rel_s4 @ sK1 @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f214,plain,
( ( $false
= ( ( q @ sK4 )
| ~ ( rel_s4 @ sK1 @ sK4 ) ) )
| ( ( ~ ( rel_s4 @ sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( ( $false
= ( ( q @ sK4 )
| ~ ( rel_s4 @ sK1 @ sK4 ) ) )
| ( $false
= ( p @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f216,plain,
( ( $false
= ( p @ sK3 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f217,plain,
( ( $false
= ( q @ sK4 ) )
| ( $false
= ( p @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f218,plain,
( ( $false
= ( p @ sK3 ) )
| ( $true
= ( rel_s4 @ sK1 @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f219,plain,
( ( $false
= ( ~ ( rel_s4 @ sK1 @ sK4 ) ) )
| ( ( ~ ( rel_s4 @ sK1 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f220,plain,
( ( ( ~ ( rel_s4 @ sK1 @ sK3 ) )
= $false )
| ( $false
= ( q @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f221,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK3 ) )
| ( $false
= ( q @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK4 ) )
| ( ( ~ ( rel_s4 @ sK1 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f223,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK4 ) )
| ( $true
= ( rel_s4 @ sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( $true
= ( rel_s4 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f228,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f229,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) ) )
| ( $true
= ( rel_s4 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X3 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X1 ) )
| ( $false
= ( rel_s4 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f235]) ).
thf(f238,definition,
( spl5_1
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f239,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f238]) ).
thf(f241,definition,
( spl5_2
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f242,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f243,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f189,f241,f238]) ).
thf(f245,definition,
( spl5_3
<=> ( ( q @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f247,plain,
( ( ( q @ sK2 )
= $false )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f248,plain,
( spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f196,f245,f238]) ).
thf(f250,definition,
( spl5_4
<=> ( $true
= ( rel_s4 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f252,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK2 ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f250]) ).
thf(f253,plain,
( spl5_1
| spl5_4 ),
inference(avatar_split_clause,[],[f199,f250,f238]) ).
thf(f255,definition,
( spl5_5
<=> ( $false
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f257,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f260,definition,
( spl5_6
<=> ( $true
= ( rel_s4 @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f262,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK3 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f265,definition,
( spl5_7
<=> ( $false
= ( q @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
thf(f267,plain,
( ( $false
= ( q @ sK4 ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f268,plain,
( spl5_7
| spl5_5 ),
inference(avatar_split_clause,[],[f217,f255,f265]) ).
thf(f270,definition,
( spl5_8
<=> ( $true
= ( rel_s4 @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f272,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK4 ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f270]) ).
thf(f273,plain,
( spl5_8
| spl5_5 ),
inference(avatar_split_clause,[],[f218,f255,f270]) ).
thf(f274,plain,
( spl5_7
| spl5_6 ),
inference(avatar_split_clause,[],[f221,f260,f265]) ).
thf(f275,plain,
( spl5_8
| spl5_6 ),
inference(avatar_split_clause,[],[f223,f260,f270]) ).
thf(f278,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ~ spl5_2
| ~ spl5_4 ),
inference(constrained_superposition,[],[f252,f242]) ).
thf(f293,plain,
( ( $true = $false )
| ( $true
= ( q @ sK3 ) )
| ~ spl5_1
| ~ spl5_6 ),
inference(constrained_superposition,[],[f262,f239]) ).
thf(f296,plain,
( ( $true
= ( q @ sK3 ) )
| ~ spl5_1
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f293]) ).
thf(f371,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s4 @ X0 @ sK3 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) )
| ~ spl5_6 ),
inference(constrained_superposition,[],[f236,f262]) ).
thf(f389,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK3 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) )
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f371]) ).
thf(f406,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $false
= ( q @ sK3 ) )
| ( $true = $false )
| ( $true
= ( p @ sK3 ) )
| ~ spl5_6 ),
inference(constrained_superposition,[],[f168,f389]) ).
thf(f417,plain,
( ( $true
= ( p @ sK3 ) )
| ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $false
= ( q @ sK3 ) )
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f406]) ).
thf(f422,plain,
( ( $false
= ( q @ sK3 ) )
| ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ~ spl5_5
| ~ spl5_6 ),
inference(forward_demodulation,[],[f417,f257]) ).
thf(f423,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $false
= ( q @ sK3 ) )
| ~ spl5_5
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f422]) ).
thf(f426,plain,
( ( $false
= ( q @ sK3 ) )
| ( $true = $false )
| ~ spl5_5
| ~ spl5_6 ),
inference(forward_demodulation,[],[f423,f224]) ).
thf(f427,plain,
( ( $false
= ( q @ sK3 ) )
| ~ spl5_5
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f426]) ).
thf(f431,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_5
| ~ spl5_6 ),
inference(forward_demodulation,[],[f427,f296]) ).
thf(f432,plain,
( $false
| ~ spl5_1
| ~ spl5_5
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f431]) ).
thf(f433,plain,
( ~ spl5_1
| ~ spl5_5
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f432]) ).
thf(f434,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl5_2
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f278]) ).
thf(f437,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK1 ) )
| ( $true = $false )
| ( $true
= ( rel_s4 @ X0 @ sK2 ) ) )
| ~ spl5_4 ),
inference(constrained_superposition,[],[f236,f252]) ).
thf(f438,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f437]) ).
thf(f485,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $false
= ( p @ sK2 ) )
| ~ spl5_4 ),
inference(constrained_superposition,[],[f438,f165]) ).
thf(f498,plain,
( ( $true
= ( q @ sK2 ) )
| ( $false
= ( p @ sK2 ) )
| ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f485]) ).
thf(f506,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $false
= ( p @ sK2 ) )
| ( $true = $false )
| ~ spl5_3
| ~ spl5_4 ),
inference(forward_demodulation,[],[f498,f247]) ).
thf(f507,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ~ spl5_3
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f506]) ).
thf(f510,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(forward_demodulation,[],[f507,f434]) ).
thf(f511,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f510]) ).
thf(f515,plain,
( ( $true = $false )
| ~ spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(forward_demodulation,[],[f511,f224]) ).
thf(f516,plain,
( $false
| ~ spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f515]) ).
thf(f517,plain,
( ~ spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f516]) ).
thf(f533,plain,
( ( $true = $false )
| ( $true
= ( q @ sK4 ) )
| ~ spl5_1
| ~ spl5_8 ),
inference(constrained_superposition,[],[f272,f239]) ).
thf(f541,plain,
( ( $true
= ( q @ sK4 ) )
| ~ spl5_1
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f533]) ).
thf(f545,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_7
| ~ spl5_8 ),
inference(forward_demodulation,[],[f541,f267]) ).
thf(f546,plain,
( $false
| ~ spl5_1
| ~ spl5_7
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f545]) ).
thf(f547,plain,
( ~ spl5_1
| ~ spl5_7
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f546]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f243]) ).
cnf(s2,plain,
( spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f248]) ).
cnf(s3,plain,
( spl5_1
| spl5_4 ),
inference(sat_conversion,[],[f253]) ).
cnf(s6,plain,
( spl5_5
| spl5_7 ),
inference(sat_conversion,[],[f268]) ).
cnf(s7,plain,
( spl5_5
| spl5_8 ),
inference(sat_conversion,[],[f273]) ).
cnf(s8,plain,
( spl5_6
| spl5_7 ),
inference(sat_conversion,[],[f274]) ).
cnf(s9,plain,
( spl5_6
| spl5_8 ),
inference(sat_conversion,[],[f275]) ).
cnf(s22,plain,
( ~ spl5_1
| ~ spl5_5
| ~ spl5_6 ),
inference(sat_conversion,[],[f433]) ).
cnf(s24,plain,
( ~ spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f517]) ).
cnf(s26,plain,
( ~ spl5_1
| ~ spl5_7
| ~ spl5_8 ),
inference(sat_conversion,[],[f547]) ).
cnf(s27,plain,
spl5_1,
inference(rat,[],[s24,s1,s2,s3]) ).
cnf(s28,plain,
spl5_5,
inference(rat,[],[s26,s6,s7,s27]) ).
cnf(s29,plain,
~ spl5_6,
inference(rat,[],[s22,s27,s28]) ).
cnf(s30,plain,
spl5_8,
inference(rat,[],[s9,s29]) ).
cnf(s31,plain,
spl5_7,
inference(rat,[],[s8,s29]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s26,s27,s30,s31]) ).
thf(f548,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO463^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:01:57 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.31 % (872650)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (872659)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=119107950:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (872661)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (872661)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.31 % (872657)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2887234318:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (872655)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=958849620:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (872656)lrs+10_16_si=on:nwc=1.5:random_seed=1229941765:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (872660)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1654751065:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (872658)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4281276111:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.31 % (872659)Instruction limit reached!
% 0.22/0.31 % (872659)------------------------------
% 0.22/0.31 % (872659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (872659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (872659)CaDiCaL version: 2.1.3
% 0.22/0.31 % (872659)Termination reason: Instruction limit
% 0.22/0.31 % (872659)Termination phase: Saturation
% 0.22/0.31 % (872659)Time elapsed: 0.008 s
% 0.22/0.31 % (872659)Peak memory usage: 11 MB
% 0.22/0.31 % (872659)Instructions burned: 26 (million)
% 0.22/0.31 % (872661)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3853698266:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (872657)Instruction limit reached!
% 0.22/0.31 % (872657)------------------------------
% 0.22/0.31 % (872657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (872657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (872657)CaDiCaL version: 2.1.3
% 0.22/0.31 % (872657)Termination reason: Instruction limit
% 0.22/0.31 % (872657)Termination phase: Property scanning
% 0.22/0.31 % (872657)Time elapsed: 0.002 s
% 0.22/0.31 % (872657)Peak memory usage: 10 MB
% 0.22/0.31 % (872657)Instructions burned: 4 (million)
% 0.22/0.31 % (872656)Instruction limit reached!
% 0.22/0.31 % (872656)------------------------------
% 0.22/0.31 % (872656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (872656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (872656)CaDiCaL version: 2.1.3
% 0.22/0.31 % (872656)Termination reason: Instruction limit
% 0.22/0.31 % (872656)Termination phase: Saturation
% 0.22/0.31 % (872656)Time elapsed: 0.010 s
% 0.22/0.31 % (872656)Peak memory usage: 12 MB
% 0.22/0.31 % (872656)Instructions burned: 19 (million)
% 0.22/0.31 % (872669)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4136539973:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.31 % (872669)Instruction limit reached!
% 0.22/0.31 % (872669)------------------------------
% 0.22/0.31 % (872669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (872669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (872669)CaDiCaL version: 2.1.3
% 0.22/0.31 % (872669)Termination reason: Instruction limit
% 0.22/0.31 % (872669)Termination phase: Function definition elimination
% 0.22/0.31 % (872669)Time elapsed: 0.001 s
% 0.22/0.31 % (872669)Peak memory usage: 10 MB
% 0.22/0.31 % (872669)Instructions burned: 6 (million)
% 0.22/0.31 % (872655) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-872650-872655"...
% 0.22/0.31 % (872661) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-872650-872661"...
% 0.22/0.31 % (872655)...printing done.
% 0.22/0.31 % (872670)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2100499567:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.31 % (872655)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (872655)------------------------------
% 0.22/0.31 % (872655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (872655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (872655)CaDiCaL version: 2.1.3
% 0.22/0.31 % (872655)Termination reason: Refutation
% 0.22/0.31 % (872655)Time elapsed: 0.020 s
% 0.22/0.31 % (872655)Peak memory usage: 13 MB
% 0.22/0.31 % (872655)Instructions burned: 37 (million)
% 0.22/0.31 % (872650)Success in time 0.056 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------